As aforestated, the goal of our work is to obtain approximate analytical solutions of the equations governing the motion of the buoy in order to gain deeper insights into the influence of the shape of the restoring force on the performance of the absorber. To achieve this goal, we will use the method of multiple scales [1]}. In order to facilitate the implementation of the method, we obtain in this section an approximation of the convolution integral governing the radiation damping in Equation (REF ).
